System for remote indication and control and automatic computation



Dec. 1'3, 1949 G. w. wALroN 2,490,391 SYSTEM FOR REMOTE INDICATION AND CONTROL AND AUTOMATIC COMPUTATION Filed March 9, 1944 4 Sheets-Sheet l v Flew.

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Dec. 13, 1949 G. w. wAL'roN 2,490,891

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Dec. 13, 1949 G. :,w. wAL'roN 2,490,891 SYSTEM FOR REMOTE INDICATION AND CONTROL AND AUTOMATIC COMPUTATION FIed March 9, 1944 4 Sheets-Sheet 4 Patented Dec'.-13, 14949 UNTED STATES PATENT oFFicE SYSTEM Foa REMO E mmon'on CONTROL vAND i TION AND AU OMATIC COMPUTA- George William Walton, Farnham Common, England Application March 9, 1944, Serial No.

In Great Britain September 3, 1941 section 1, Public Law ssn, August s, 194e Patent expires September 3, 1961 Claims. '(Cl. 177-351) This invention relates to a' discovery of and systems for automatic computation employing remote indication and control and the like and of the operative signal is of paramount importance and no dependence can be placed on inten'- sity, phase or frequency .of a single component signal. In every such system the essential feature is that a magnitude .be related to a dimension of the signal either linearly`y or in accordance with some mathematical function which is predetermined, pre-arranged or imposed by an inherent characteristic of the apparatus used. Clearly the dimension of the signal to which the magnitude is related must be one which cannot vary except within prescribed limits and those limits are dictated by the precision required. Time is one dimension of every signal which in itself does not vary but there is no constant scale on which time can be measured for the only -way time can be appreciated is by sequence of events and such a sequence is not constant, i. e. it is an elastic measure which may stretch and contract erratically, and therefore'if a magnitude is related to time it must be accompanied by the time-scale on which that time is measured.

In systems for automatic computation employing remote indication and control a magnitude may be Very precisely related to a constant dimension of the signal by suitable apparatus but other apparatus cannot reproduce that magnitude with equal precision unless there are a sufcient number of items of information in the signal,'the first said apparatus incorporates means for producing those items in the signal and the said other apparatus incorporates means which can use all those items in reproducing the magnitude, i. e. those items in a mathematical sense correspond to the signicant digits in a number.

Systems for precise automatic computation employing remote control where appreciable power is necessary to move a body in accordance with a magnitude related to the signal require servo operation and means therefor in many cases must be responsive to rates of change of an original magnitude, i. 4e. those means must be capable of diilerentiating a variable with respect to time at least up to a predetermined order of differential co-emcient with respect to time, if the'reproduc tion of the magnitude as movement of the body is ynot to lag to an extent which destroys the instantaneous precision of relation to the original magnitude related to the signal. YThis differentiation is yadditionally or alone of importance in automatic computation,

The most simple form of any system for automatic computation employing remote indication and control is one which comprises one station producing a signal and one station using that signal and only one magnitude is related to a dimenf sion of the signal according' to some mathematical function. That one magnitude may be the sum, difference, product, quotient or resultant of two or more magnitudes or it may be a factor, component, power, root or the like provided that means are associated with the producing station for deriving the magnitude to be related to a dimension of the signal from one or more than one original'magnitudes. When the nature of the signal used vin such a system is of a form which permits ready compounding with and/or variation by another such signal, with the corollary thereof that two or more signals can 4be derivedfrom one such signal, then the scope and usefulness of the system is greatly enhanced, e. g. a. number of stations producing signals may take part in the control of one or more than one station using signals in a manner which no one of the stations producing signals could do alone.

Such a compound system clearly constitutes means for automatic computation whether or not remote control and/or indication is simultaneously performed by it, every signal used therein corresponding, in eiect, to a number (which has a number of significant digits according to precision) which enters into the computation.

Hitherto computing machines have lbeen manually operated and could `only deal with constant magnitudes. Attempts have lbeen made to evolve computing apparatus capable of dealing with a number of variable magnitudes .but such success as has been achieved has been severely limited by lack of precision. Systems for automatic computation employing remote control and indication must be capable of dealing with variable magnitudes and if precision can be obtained to any predetermined limits then a compound system according to the last paragraph above would be capable of automatic computationl with any number of constant and/or variable magnitudes toany required limit of accuracy and theifrapidity of computation would be so great thatfor most practical purposes it can be regarded as instantaneous.

It is an object of the present invention'to.

provide a system for automatic computation employing remote indication, and control whichcomprises means for relating a. magnitude to time in a signal which contains the time-scale onl which that time is measured and means for reproducing that magnitude according to a mathe matical function from that signal.

Another object of the invention is to provide.

in such systems means for measuring a magnitude on a plurality bf diierent scales and relating the several scales .ofmagnitude'to at least time in onesignal. for the purpose ofincreasing precision. and means for reproducing a magn'ztude related to the original magnitude according to a mathematical fi'nction from the said s'gnal.

Another object of the invention is to provide in such systems means forreproducing -a magnitude related to an orginal magnitude by relating a plurality of 'magnitudes on different scales to at least time in 4one signal the said plurality of magnitudes being combined to form the said reproduced magnitude for the purpose of increasing precision in reproduction.

" Another object of the invention is to provide in v auch systems means responsive to rate of change of a varying magnitude. j

Another object of the invention is to provide in such systems means for comparing time intervals of two signals and deriving therefrom a signal related to any diiierence of the said time intervals.

'1"hel principal object of the invention is to provide a system for automatic computation which employs signals in transferring magnitudes entering into the processes of computation, control and indication and'which comprises any number of signal producing devices and` any number of intermediate devices producing, using, converting and combining signals which in co-operation provide signal control of any number of signal using devices the magnitude reproduced by each thereof being related. according to a predetermined mathematical function to ai least one original magnitude or to a magnitude which is the result of automatic computation in said system.

The invention will now be described making l Fig. 2 is a diagram of the circuits of the instrument of Fig. 1 which deal with oscillations.

Fig. 3 shows a modified form of cathode-ray tube used in the instrument of Fig. 1 and shown inFig. 2.

Fig. 4 is an explanatory diagram showing in graphs the relations between oscillations in the circuits of Fig. 2 and the associated impulses in the circuits of Fig.' 5.

Fig. 5 is a diagram of circuits of the instrument I of Fig. 1 which deal with impulses.

Fig. 6 is a circuit diagram of an instrument for comparingtwov signal components and deriving therefrom-a dinerential response.

. Fig. 7 is vafdiagram showing in graphs examples loi' relations between signal components in the instrument of Fig. 6 and the resulting differential responses.

Fig. 8 shows an arrangmeent of iluid valves responsive to differential responses provided by the instrument of Fig. 6 which control servo reprof duction of a magnitude.

Fig. 9 shows diagrammatically multiplication and division of a magnitude by' change of the time-scale of its signal.

Fig. 10 shows diagrammatically the laddition vand subtraction of two magnitudes by combining ktheir signals in a case when the signals have a common component.

Fig.' 11 shows diagrammatically the addition and subtraction of one magnitude to and from another magnitude.

Fig. 12 shows instrument circuits for multiplication and division of magnitudes by change of signal time-scale.

Fig. 13 shows diagrammatically the combination` of a plurality of signals by intcrspersal of impulses.

Fig. 14 shows instrument circuits for combining two sr',nals by interspersall oi impulses.

Fig. 15 shows an' example of a device forrelating a linear magnitude to an angular magnitude. Y

Figr 1 6 shows an example of a device for relating an angle to the logarithm of the sine or ccsine plus one of that angle, a linear magnitude tothe logarithm of that magnitude and alinear magnitude to an angle.

Fig. 17 shows an example of a device for relating an angle to the logarithm of that angle and for relating a linear magnitude to the logarithm thereof as an angle,

In Fig. 1 a signal producing instrument I is associated with a phase displacing mechanism which has the shafts 2 and 2a which have bearings in the frame 3 and on the shaft 2 are the vgearwheels 4 and 5 which mesh with the pinion 6 xed on the shaft 2a. The gearwheel 4 is iixed to the shaft 2 and a spring I is fixed to a lug 8 integral with 4. The springl I applies pressure to a lug 9 integral with the gearwheel 5 which is otherwise free t'o turn on the shaft 2 so that as 4 and 5 both mesh with 6v backlash is prevented between 2 and 2a when the pressureA of I is greater than any torque applied to 2. Fixed to the shaft 2 is the polyphase armature Ill co-operating with the statorv II xed to 3 and xed to the shaft 2a is the polyphase armature I2 co-operating with the polyphase stator I3 which is fixed to 3. The amature I0 has the sliprings I4 and the brushes I5 held by an extension of 3 and the brushes I5 are connected to the terminals I'I of the instrument I. The terminals i8 of the polyphase stator II are mounted on the insulating block I9 and are connected to the terminals 20 of the instrument I. The armature I2 similarly has the sliprings 2I and brushes 22 connected to terminals 23 of I and the stator I3 has the terminals 24 on insulating block 25 connected to terminals 26 of I. The mechanism above described constituting -means for relating a magnitude to a plurality of .spatial magnitudes. i, e. angular displacement o 2 to the angular displacements of I0 and I2 rela tive to I I and I3 respectively. lThe instrument I supplies polyphase oscillations to II and to I3 each of which forms a rotating magnetic eld and the direction of the rotation of the Afields can be reversedbyfthe" double reversing switch I6. e. g. with two/phaseA supply by reversing one phase.thereof. The phase of oscillations-induced in the armature I to II and if the shaft 2 is rotated through an angle then the phase of the oscillations at I1 will be advanced or retarded by a corresponding angle relative to the 'phase of .oscillations at 20 but the angular movement lof 2 is a magnitude-and theref, and'lfocusing cylinder or v.of cathode rays is focused electrostatically and '10,

fore that magnitude is related to a phase angle of oscillations by I U-II. The shaft 2a has a constant ratio of gearing to the shaft 2 and therefore the magnitude of angular displacement of 2 is related to a greater magnitude of angular'disl placement of 2a accordingto the gear ratio :between the shaftsand because of I2-I3 to` a phase displacement between` the oscillations 4at' 23 relativeto those at 26, i. e. a magnitude of angular movement of 2 causes two phase displacements one of which is a multiple of the other. The production and use of oscillations in the instrument I of Fig. l can be better understood from Fig. 2 in which a multios'cillator unit 46 of known kind provides, in the present example, two

distinct oscillations one`being 4a harmonic of the other The lower frequency oscillation is sup'- plied by 40 to a phase-splitter 4I of known kind which supplies polyphase -oscillations at that frequency to the known kind of phase adjuster 21 and that in turn supplies the polyphase oscillations to the stator II. Similarly supplies the higher frequency oscillation to the known kind of phase-splitter 43 which. supplies polyphase oscillations at thesame frequency to the known kind of phase adjuster 28 and that in turn supplies the polyphase oscillations t0 the stator I3. The polyphase oscillations induced in the armature I0 are supplied to the deectingplates of the cathode-ray tubes 36 and 45 thereby causing circular sweeps of the beams of cathode rays therein and similarly the oscillations induced in the armature I2 are supplied to the deecting plates of the cathode-ray tubes 31 and 46 producing circular sweeps of their beams of cathodev rays. Any angular movement of the shaft 2 inI Fig. l will simultaneously produce advance or retard of the sweeps of the beams of cathode rays in 36, 31, 45, and 46 which, if I0II -and I2-I3 are single-pole, will in 36 and 45 .be equal to the angle of movement of 2 and in 31 and 46 will be a multiple of that angle of movement. Polyphase oscillations are supplied by 4i through leads 42 to the deecting plates of the cathoderay tube 41 and by 43 through the leads 44 to the defiecting plates of the cathode-ray tube 48 to produce circular sweeps of the beams of cathode rays in those tubes those sweeps being unaffected in phase by I6, 21, 28, I0-II or I2-I3. The phase sequence reversing switch I6 of known kind simultaneously reverses connections to one phase of the terminals 20 and of one phase of the terminals 26 thereby reversing the direction of sweeps in 36, 31, and 46 so that the angle of advance or retard of the sweeps of thosel tubes vcorrespond to an equal angle of retard 0r advance respectively. The phase adjusters 21 and 26 are for calibration purposes as by means of them constant angles of advance or retard can be added or subtracted to or from the sweeps of 'the tubes 36, 31, 45 and 46.

In Figs. 2 and 5 the cathode-ray tube 36 cooperates with 31, 45 with 46 and 41 with 48 the rst `of `each of those pairs having the lower frequency v,oi sweep. "h

vfluorescent screen but 45, 46. 41 and 46 are of a modied kind' shown in is no fluorescent, screen.

Fig, 3 in which there tems having a cathode, anode, control 'electrode cylinders when the beam deflector plates when electrostatic deflection is employed the electrodes of the system being connected in the usual way to pins 5U in the base 6I. Magnetic focusing and/or deflection of the cathode ray beam in the well known manners maybe used with cathode-ray tubes in the present invention but electrostatic focusing and deflection-is simpler in the small inexpensive tubes which are entirely satisfactory for the purposes of the present invention. In Fig. 3 the envelope 49 is shown partly cut away to expose the target electrode 52 which takes the place of the nuorescent screen in 'ordinary'cathode-ray tubes. The target electrode 52 is mounted inside the tube to be edge on to the cathode rays and is a thin plate of metal iixedto the support 53 which is electrically connected to the cap 54. The target electrode 52 is radial to the axis of thetube and the cathode rays are focused in the plane of 52 vwith a circular-sweep of the beam so that when every revolution vof the cathode ray beam whenV thecathode rays fall o n 52.

The device of Fig. 3 as used in the instrument I of Fig. 1 and shown in Figs, 2 and 5 plays a very important part in securing increased precision which will-be better understood from Fig. 4.. If the curve 55 in Fig. 4 represents one phase of oscillation supplied to 41 in Fig. I2 and the curve Blirepresents the corresponding phase of oscillation applied to 45 in Fig. 2 then it is clear that the time interval -between the peak 51 of 55 and the peak 62 of 60 is accurately related to the angular displacement of the shaft 2 in Fig. 1 if 51 and 62 are coincident in time when angular displacement of 2 is zero. The absolute value of the time interval between 51 and 62 may vary from cycle to cycle of the oscillations 55 and 60 if the frequency of the oscillations 55 and 60 varies so that angular displacement of 2 is not accurately related toan interval of absolute time but is accurately related to the ratio of time intervals t/p if t is the absolute value of the time interval between 51 and 62 and p is the absolute value of the period of the one cycle of the oscillations 55 and 60 in which t is measured, i. e. p provides the immediate time-scale on which t is to be measured. The oscillations 55 and 60 are both produced .by the one oscillatorw in Fig. 2

and therefore with undisturbed adjustments of time interval t on the time-scale p but a second angular magnitude exactly equal to the originalv angular magnitude cannot be reproduced from the oscillations 55 and 60 because the ratesof change of intensity about the peaks 51 and 62 are very small and any apparatus used must be dependent on changes of intensity. The device l The envelope 49 in Fig. 3 contains any oi. the well known electrode sysspot of cathode rays and the thickness of 52 at 5 the radius of sweep and the angular velocity of the sweep so that the time duration may be a very small fraction of the period of the sweep. Also the duration of the impulse is not affected by i its intensity and the period between two sucl` cessive impulses is exactly equal to the period of the sweep no matter if the radius thereof varies or is elliptical or irregular.

, In Fig. 2 the tube 44 co-operates with the tube 41 but the sweep of 44 is at a higher frequency 15 so that the duration of an impulse in its target electrode circuit relative to the -duration of an impulse in the' target" electrode -circuit of 41 is in the same ratio as the periods of sweep of 4l to 41. The curve 55 shows one phase of oscilla- 2 tion applied to 41 .and the curve 56 one phase of the oscillation applied to 4I and if the positive` peaks of both are in phase at 51 and at that instant 41 and 48 both have impulses in their target electrode circuits then as 5l is a harmonic 25 of 55 the double impulse will be produced only once per cycle of 55. The impulse o f 41 can limit the impulses produced by 4l to one per cycle of 55 at the instant 51 as shown by y58 in Fig. 4

in which the points 59 show the instants at which 30 4I would produce other impulses but for the limiting action of the 41 impulse. The result of this is that 5 4 is a train vof impulses with a period exactly equal to the period of 55 but with the impulse duration of the tube 4t which can be 35 very small in view of the fact that the period of sweep in 48 may be equal to or appreciably less v than the duration of the impulse of 41. In the same way the tubes and 48 provide a train of impulses with the period of 60 and 55 and .m

the duration of impulse d ue to 45, 50 being the curve of one phase of oscillation applied to 45, 5| being one'phase of the oscillation applied to 46 which is in phase with 50 at the instant 52.

4s and as both producing impulses at the instant 4g 52, the impulse of 45 limiting impulse produced by 45 to that at the instant 52 as shown in 53 in which the points 54 show the instants at which 45 would produce other impulses but for the limiting action of the 45 impulses. The oscilla- 50 tion 6| in frequency is a multiple of Il that multiple being equal to the gear ratio between 2 and 2a in Fig. 1 so that movement of 2 time phase displaces 50 and 5I equally, i. e. a positive peak of 5i is always in phase with the positive peak 55 of however 2 is moved and the impulses produced by 45 and 4B are always at the instants 52.

The impulses 5B may be negative and the impulses 63 positive as shown in Fig. 4 so that they can be directly added to form one intermittent 60 signal 65 comprising two distinct components which can be readily separated by simple rectifiers or limiting valves. Each train of impulses 58 or 63 is a cosine series of harmonics the fundamental having the period of 55 and the 65' number of harmonics being approximately equal to the fundamental period divided by the duration of one impulse. Each of those harmonics is anv additional item of information relating to thetime-position of the impulses and therefore to the value of the time interval t between a variation or impulse of 5I and a variation or impulse of 63, i. e. between 51 and 42, and also of the period p between successive variations or 'Modaal reference component and from these 'the ratio -t/p which is precisely related to the magnitude of angular displacement of the shaft 2 in Fig. 1. The precision with which the ratio t/p can be obtained from the signal 65 depends on the number of stages geared together in the instrument of Fig. l, in Fig. 1 there are two such stages the first comprising IU-II. 45 and 41 and the second stage comprising l2-I3, 48 and 48. Even in one stage the tubes 45 and 41 give greatly increased 'precision as will be-appreciated from Fig. 4 for suppose 55 and 50 were transmitted to a distant station then each must have a channel of its own and at that station the phase diil'erence'V ties but with 45 and 41 in that stage as small ,tubes with a radius of sweep of one centimetro precision can be increased 50 to 100 times and with larger tubes having more than l0 centimetre radius of sweep precision could be 1000 times better. With three or four geared stages using small tubes an accuracy of one second of I in automatic computation, particularly as it can.

be related to a magnitude having any variation without reduction of that precision.

Fig. 5 shows one example of circuits of the tubes 45, 46, 41 and 48 of Fig. 2 for producing impulses as described in connection with Fig. 4

s and for the tubes 35 and 31 in Figs. 1 and 2 which uses cathode resistors and direct connections between tubes for the purpose of minimising phase distortions of the impulses. of A. C. is connected to the terminals 66 of a transformer primary 51 the transformer having a number of separate secondaries of which 65 supplies heaterjcurrent to the heaters of all the tubes and valves. All of the other secondaries are associated with rectiiiers and smoothing.

circuits for the supply of D. C. to the electrode circuits of the tubes and valves. The secondary 59 through rectifier 10 suppies anode potential to tubes 45 and 41 the negative being connected to the 4cathode resistors 1| and 12 to the cathodes of 45 and 41 respectively the grids of those tubes being connected to that negative. No signal is applied to the grids of 45 and 41 so that they operate with constant intensity of the cathode ray beams potential drop across 1I and 12 providing negative bias to the respective grids so that the desired intensity of the beams is obtained. The target electrode circuits of 45 and 41 have an independent D. C. supply provided by the rectifier 13 and the secondary 14 the negative return being through the target electrode circuit resistors 15 and 16 respectively of 45 and 41. The cathodes of 45 and 41 are direct connected to the grids of 45 and 48 respectively and negative cut-oil bias is applied to those grids by the rectiiiers 13 and secondary 11 across the resistor 18 in the case of 46 and by rectifier 13 and secondary 19 across the resistor 80 in the case of 48. The anode circuit of 46 is supplied with D. C. by the secondary 8l and rectifier 1l with negative return direct connected to the cathode of 45 and the anode circuit of 48 isll impulses of 5t or 53 whichever is used as the 7s plied with D. C. by the secondary lla and recti- In Fig. 5 a source 9 ner 18 with negative return direct connected to the cathode of 48.

The tube 4s is massed to cut-on' and therefore no cathode rays can fall on its target electrode -until a positive potential is applied to its grid oi' 41, i. e. when cathode rays fall on the target electrode of 41 producing a potential across 18 thereby applying a positive potential to the grid of 43.

The target electrode circuit of 46 is supplied with D. C. by the secondary 14 and the rectifier 82 with negative return from the cathode of 46 through the output resistor 83 across which a potential is developed when cathode rays fall on 52 of 46. The target electrode circuit of 48 is supplied with D. C. by .the secondary 64 and the rectifier 85 with negative return from the cathode oi' 48 through the output resistor 86 across which a potential is developed when cathode rays fall on 52 of 48. 'I'he terminals 30 (Figs. 1 and 5) are connected to the ends of the resistor 86 and from them can be taken the train of impulses produced by 48 in the form of 58 in Fig. 4 and the terminals 3l (Figs. 1 and 5) are connected to the ends of the resistor 83 and from them can be taken the train of impulses produced by 46 in the form of 63 in Fig. 4. The resistors 83 and 86 are connected in opposite sense with the terminals 32 (Figs. 1 and 5) connected to the free ends of 83 and 86 and from those terminals can be taken the signal in the form of 65 in Fig. 4 due to the addition of the trains of impulses produced by 46 and 48. The whole of the electrical part of the Fig. 1 instrument constitutes means for relating a plurality of spatial magnitudes to the t/p ratio of a signal.

'I'he instrument of Figs. 1, 2 and 5 may be used as a producer or as a user of signals, the whole arrangement of Fig. l-being used in control of movement of a body with or without automatic computation and similarly only the instrument l. of Fig. 1 for indication of the value of the t/p ratio contained in a signal with terminals i1 connected to and 23 connected to 26. For such control or indication the terminals 33 Fig. 5 have the incoming signal applied to them one being connected to the grid of the valve 88 and the other to the grid of the valve 89. The secondary 90 and rectifier 9| supply negative bias to the grid of 88 across a resistor 92 connected between the grid of 88 and the cathode of 89. Similarly the secondary 93 and rectifier 94 supply negative bias to the grid of 89 across a resistor 95 connected between the grid of 89 and the cathode of 88. The secondary 14 and rectifier 82 supply D. C. to the anode circuits of 88 Aand 89 with negative return from the cathodes thereof through the resistors 91 and 96 respectively and the resistor 81. When a signal such as 65 in Fig. 4 is applied to the terminals 33 one component produces a train of impulses across 96 and the other component a train of impulses across 91 and by means of the reversing switch 39 (Figs. 1' and 5) 96 can be connected across the terminals 34 with 91 connected across 35 or vice versa; i. e.

l0 the components ci' the signal are separated with one at 34 and the other at 35.

The ordinary cathode-ray tubes 36 and 31 are for visual indicating purposes and have their anodes connected together, their grids connected together' and their cathodes connected together anode current being supplied by the secondary 14 and rectifier 82the cathode resistor 81 providing negative grid bias to the tubes 36 and 31. By means ot the switch 38 the train of impulses at terminals 3| can be applied to the grids of 36 and 31 or the train of impulses at terminals 35 can be applied to those grids the former affording indication when 45 and 48 are in time-phase during signal production and the latter during indication of the t/p ratio of a signal supplied to the terminals 33. During such indication impulses at terminals 34 are applied to the oscillator 46 in Fig. 2 for the purpose of synchronising and phasing the oscillations produced by 40, i. e. those oscillations are brought into the same phase at the same fundamental frequency as the train of impulses. The train oi impulses at terminals 36 are also applied to 40 as a kind of feed back which not only tends to stabilise the frequency and phase of the fundamental frequency oscillation supplied to 4| in Fig. 2 but also controls the frequency and phase of the harmonic oscillator in 40 which supplies the oscillation to 43 without any direct control by the fundamental oscillator in 46 for the train of impulses at 36 is a cosine series of harmonics rigidly linked to the fundamental so that each of the harmonics is in exact time-phase with the fundamental and has a frequency which is an exact multiple of the fundamental and therefore as that series must include a harmonic with a frequency equal to that of the harmonic oscillator in 40 there can be no better means of controlling that oscillator than that train of impulses.

The operation of the tubes 36 and 31 will be best understood in the case of calibration and indicating the t/p ratio of the signal in signal production with the apparatus of Fig. 1 in which the ends ol' the tubes 36 and 31 have circular scales each with ten divisions and if the gearing between 2 and 2a is 10 to 1, the circular sweep in each tube is clockwise and the negative bias applied to the grids of the tubes by 81 in Fig. 5 is such that without positive impulses applied to those grids the trace of the cathode rays on the screens of the tubes is barely visible then when the train of impulses at terminals 30 is applied to the grids of the tubes by the switch 38 and connecting terminals 30 and 35 a bright point will appear on the screen of each tube in the path of the sweep of the cathode rays in each. Those points will be little larger angularly than the focused spot of the tubes because of the short duration of kthe impulse and they will not be continuous but will appear simultaneously in each tube at the frequency of the train of impulses, if that frequency is more than 20 cycles per second the points will appear to be continuous because of persistence ofv vision. With the shaft 2 in Fig. 1 stationary the bright point on the screen of 38 can be moved to any angular position in the circular scale by adjustment of 21, e. g. to the long zero line, and similarly the bright point on the screen of 31 can be moved to any angular position in its circular scale by adjusting 28. The controls 21 and 28 are for cali` brating the instrument, e. g. in Fig. 4 moving 82 until it is coincident with 51 or at a desired time interval from 51 the control 28 bringing 6I into phase with 60 thereby obtaining the strongest i3 impulses and the brightest points on the screens of 36 and 31.

Suppose the bright points are brought onto the zerolines of their respective scales in 36 and 31 then any movement of the shaft 2 will cause the bright points on the screens of 36 and 31 to move circularly over their respective scales the movement in 31 being ten times greater than in 3B, i. e. one division in 36 would be accompanied by the full ten divisions in 31 and therefore each division in 31 is equal to a tenth of a division in 35. By means of the two scales it is possible to read oil' any angular movement to 54 minutes the scale of 36 giving multiples of 36 degrees in the number of complete divisions through which its bright point moves, `the scale of 31 giving additionally multiples of 3.6 degrees up to the tenth multiple in the number of complete divisiom through which its bright point moves and a quarter of a division in the scale of 31 can be readily estimated. With quite small tubes 36 and 31- there may be 60 to 100 divisions of each scale and at 60 divisions per scale the angle of movement of 2 could be read to an accuracy of 3 minutes and if the instrument of Fig. 1 had three geared stages as previously explained there would be a I. alone control that local energy or third tube such as 31 with which the accuracy,

could be 3 seconds and with a fourth such stage the accuracy would be 0.05 second. The indications provided by the tubes 30 and 31 depend on timeand are wholly independent of intensity of the bright point or the deilecting fields of 'the tubes and the sweeps of the tubes may be elliptical, varying in radius, irregular or may have a ripple without affecting accuracy.

12 the rate at which that energy is used, i. e. the power, for the ratio t/p is solely a matter of time. The extent to which a control body is moved is a magnitude which can be precisely related to a t/p ratio in a signal according to the invention and therefore much greater precision of control can be obtained by checking that magnitude by relating it to a t/p ratio, comparing that ratio with that of the received signal and using any error to control the local energy, i. e. the control of the local energy is a secondary matter which need not be particularly precise.

Suppose the controlled body is a spindle which 'it is required shall b at the same angular displacement around its axis from some zero reference angle thereof as is' the shaft 2`in the instrument of Fig. 1 which produces xthe signal to be used for control, then coupled to that spindle must'be a servo device for turning it and means for controlling the servo device as hereinafter described. VAt the point of control an instrument as in Fig. 1 would be used with its shaft 2 coupled to the said spindle and the incoming signal from thel distant transmitter would be applied to the terminals 33 of the instrument at the point of control the components of that signal appearing at the terminals 3l and 35 respectively. The instrument at the point of control would be cali- The instrument of Fig. 1 used for final indication in automatic computation or in remote indication has terminals I1 connected to terminals 20 and terminals 23 connected to terminals E the incoming signal, produced by a distant instrument such as-that of Fig. 1, is applied to the terminals 33 and the component of that signal at the terminals 34 controls the oscillator 4I and therefore the sweeps of the tubes 33 and 31 whilst the component of the signal at terminals 35 is applied by means of the switch 33 to the grids of those tubes. When first brought into operation the receiver is calibrated as described above and -brated as described above by applying the impulses at` 35 to the grids of tubes 36 and 31 by means of the switch 3B, vturning the spindle and therefore 2 to zero angle if calibration is to be at zero and adjusting 21 and 28 so that in either position of switch 33 the same reading is obtained from- 36 and 31. After calibration whatever the angular displacement of the spindle there will be a train of impulses at the terminals 3l displaced by a time interval t from the impulses at 34 measured on the time-scale p which is the period of the impulses at 34l and the impulses at 35 are similarly displaced by a time interval from those at 3| which is also measured on the same timethereafter the tubes 36 and 31 provide a continuonsuilicient shortness of duration of the individual impulses in the signal, the radius of sweep in the tubes, the number of divisions in their circular scales and the number of tubes such as 35 and 31. The instrument of Fig. 1 therefore constitutes means for reproducing one or a plurality of spatial magnitudes relateduto the t/p ratio of the signal.

Final or other control in automatic computation requires the movement of something which may be small and needing little power to move it or it may be large and heavy so that considerable power is required to move it. In either case the signal used in the invention cannot be *satisfactory as power for accomplishing-movement of a body for even after considerable amplification the energy of the signal is small and is less with increased precision and furthermore that energy is in no way related to the essential information in the signal, i. e. the t/p ratio. Clearly at a point of control there must be a local source of energy, such as electric, hydraulic, `compressed air, heat and the like, which as a means of servo action eects movement of a control body. The signal is not of a form which can directly or 0f itself scale p. Clearly the impulses at 3| can be directly compared with those at 35 instead of comparing the t/p ratio of the 3|-34 signal with that of the 35-34 signal and if there is no time interval of displacement between the 3| and 35 impulses then the angle of displacement of the spindle at the point of control is the same as the angle of displacement of the shaft 2 at the signal producing instrument within the precision of the system in use. Should the angular displacement ofthe spindle at the point of control 'be different to that of the shaft 2 at the signal producing instrument the 3| impulses will have a time interval of displacement from the 35 impulses and if that time interval or error is e then the angular error of the spindle displacement will be plus or minus 360 e/.p degrees if phase displacers such as I0|| in Fig. 1 are all single pole.

Fig. 6 shows an example of circuit diagram of an intrument for comparing the 3| and 35 impulses and deriving therefrom a differential response the mean energy of which is approximately proportional to e/p as described in the last paragraph above. In Fig. 6 a source of A. C. is connected to the terminals 98 of the primary of a transformer one secondary of which supplies current to the heaters of all of the valves and the other secondary through rectifier 39 supplies anode current to the valves |0|, |04, |08 and ||0 and through the rectifier |00 supplies negative grid bias to the valves |08, H0, Ill, ||5, IIS and l|1. The cathode of I0| is connected 16 to a coil |02 connected across the terminals |03 13 and the cathode of |04 is connected to a coil |05 connected across the terminals |08 the coils |02 and |05 being in parallel and each in series with the resistor |01 to the negative return of the anode current supply.v The coils |02 and |05 would normally be external to the instrument, e. g. they would be the windings of an electromagnetic device as shown in Fig. 8, and be simply connected to the terminals |03 and |06. The anode of |08 is connected to the grid of |0| and |08 is supplied with current through the resistor |09 so that when a heavy current ows through |08 there is a voltage drop across |08 and a cutoiI negative potential is applied to the grid of Similarly a cut-off negative potential is applied to the grid of |04 when a heavy current ows through I I0 and theresistor III. The valve ||4 normally biased to cut-olf when a positive impulse isapplied to its grid becomes conducting and charges the condenser ||2 to the voltage across the resistor I|8 the charge of ||2 opposing the negative bias applied to the grid of |08 |0| is at cut-oi and similarly a positive impulse applied to the grid of the valve ||5 charges the condenser I I3 so that I I0 is at low impedance and |04 at cut-oil'. The valve ||6 is biased to cut-off and therefore ||2 cannot discharge through it and similarly ||3 cannot discharge through the valve ||1.

Suppose that the .two trains of impulses are applied to the terminals 3| and 35 respectively and that an impulse at 3| is earlier than the next impulse at 35 then a positive impulse is applied to the grids of the valves I|5 and H6 then the former will charge the condenser ||3 and the latter will discharge the condenserl I2 so that |0| becomes conducting and |00 is maintained nonconducting and both will remain in those states until a positive impulse is applied to the grids oi`- the valves Il and |I'| on which the condenser I I2 will be charged but ||3 will not discharge because the resistor |01 due to current through |0| applies a positive potential to the cathode of which is equal to or more than the potential of |I3 and in eiect an increased negative bias is applied to the grid of not be discharged by This action will continue so long as the 3| impulses are in advance of the 35 impulses and the result will be better appreciated from the graphs of Fig. 7 in which ||9 represents the 3| impulses and 20 the 35 impulses and the resulting current in the coil |02 is shown by I 2|. Each o'f the rectangular impulses in |2| is started by a 9 impulse and continues until ended by a impulse so that the duration of a |2| impulse relative to the period of the impulses is proportional to e/pY and therefore the mean energy in the I 2| impulses is equal to e/p. The |2| impulses can be used to control the servo drive of the spindle at the receiver so that the spindle is rotated until there is no time interval between the ||9 and |20 impulses at which there will be no current in the coil |02 in Fig. 6 or there will be opposing currents in |02 and |05 which is equivalent to no current for those coils are in practice one coil with a centre tap.

If the 3| impulses lag behind the 35 impulses then in Fig. 6 the latter will initiate current ow through the coil i 05 and the former impulses will terminate that ow as shown in Fig. 7 Where |20 represents the 35 impulses and |22 the 3| impulses and I 23 shows the rectangular irnpulses in the coil |05. 'I'he mean energy of the |23 impulses is proportional to e/p and is negative to the I|2| impulses so that across the pair of coils |02 and |05 in Fig. 6 a diilerential current is produced with a mean energy proportional to plus or minus e/p and that current can be used to diierentially control the servo drive of the spindle at the receiver so as to adjust the angular displacement of that spindle until it is equal to the angular displacement of the shaft 2 at a distant transmitter.

The valves |0| and |04 in Fig. 6 may be gas relays if a strong differential response is required. The differential response of the arrangement of Fig. 6 may in some cases provide powerfor the servo drive of the spindle in the example described above. Fbr example a D. C. electric motor having a permanent magnet field of a well known kind may be geared to the spindle so that the impedance of |08 is low and so that ||3 canv tion increases error.

with its armature brushes connected across the pair of coils |02 and |05 in Fig. 6 the differential response of which will not only decide the direction of rotation of the motor and therefore of the spindle but also the speed and power'of the motor for when the error of the angular displacement of the spindle is great'the speed and power of the motor will be high but when that error is small the speed and power of the motor will be small, i. e. a characteristic which is very desirable in automatic adjustment of theangular displacement of the spindle. Clearly Fig. l together with Fig. 6 constitutes means for relating a spatial magnitude, i. e. displacement ofthe spindle, to the t/ p ratio of a signal.

'I'he above example of means for servo adjustment of the angular displacement of the spindle would not be satisfactory in a case where it is necessary that there be a minimum or no lag in the angular adjustment, for example when that displacement must vary continuously and the instantaneous angular displacement of the spindle at the point of control must be equal to the angular displacement of the shaft at the signal producing instrument within very small limits. If the magnitude at the signal producinginstrument is varying then the reproduced magnitude at the point of control must also vary which means that the servo adjustment must be in operation continuously during the variation and therefore there must be a differential response from the instrument of Fig. 6, i. e. that response cannot be zero, but there can be no such response without a plus or minus e/p error and if there is an error the reproduced magnitude cannot be instantaneously equal to the original magnitude. Furthermore increased rate of change of varia- -Fig. 8 shows one example of servo means for adjusting a continuously varying magnitude.

In Fig. 8 a hydraulic pump |24 supplies uid at pressure through the pipe |25 to a valve |2`||28 and a valve |39 low pressure discharge from the valves being returned through pipe |26 to |24. The ilrst of these valves is shown sectioned in a plane normal to its axis and consists of a body |21 with a cylindrical bore in which turns a cylinder |28 which has two diametrically opposite segments of annular grooves one of which is supplied with fluid under pressure by |25 and the other has uid at low pressure and is in communication with the pipe |28. Between the groove segments l|28 is solid. In |21 the cylinder |28 is turned by an arm |29 rigidly xed to |28 and |29 is moved by a double solenoid having 'the windings |02 and |05 in which move the plungers |30 and I3| respectively the plunganziani ers lbeing rigidly filled to a rod |32 which is free to slide in qholes in the members |33 and |34 which are rigidly fixed to the body |21 and to the iron case of the solenoid |02-|05. In the rod |32 is a pin |35 which engages `in a slot in the end of the arm |29 and without energlsation of |02`or |05 the arm |29 is held in the mean positlon,as shown in thedrawing. by the limited springs |36. In the bore ofthe body |21I are two recesses each opposite a solid part of |28 when in the mean position and one of these recesses is in uid`communication with the pipe |31 and the other with the pipe |38.

When current iiows in the winding |02 in Fig.l

the pressure of one of the springs |35. When a' current flows in the winding |05 the same action occurs but with opposite movements so that |31 communicates with |26 and |38 with |25.

The second valve |39 in Fig. 8 is similar in structure and operation to the |21-|28 valve except that it is hydraulically operated by means of a plunger |40 having a pin |4| engaging in the slot in the end of the arm |29 the plunger |40 being double ended and sliding in the cylinders |42 and |43 which are rigidly xed to the body of |39. The pipe |31 is in fluid communication with the cylinder |43 and the pipe |38 with the cylinder |42 so that when |02 is energised fluid under pressure is supplied by |24 through |25, valve |21- |23, pipe |31 to cylinder |43 thereby forcing |40 outwards from |43 and inwards in the cylinder |42 iluidin which flows through |38, |21-|28 and |26 to the pump |24. The movement of |40 n operates the valve |39 putting |25-into uid communication with |44 and |26l into uid communication with |45. A multi-cylinder hydraulic engine |46, of wellknown kind, with a shaft |41 is thereforesupplied with fluid under pressure through |44 and discharges that iiuid at low pressure through |45 and |41 will rotate in one direction. The direction of rotation of |41 would be reversed if |05 were energised instead of |02 for then iiuid under pressure would be supplied through |25, |21-|28, and |38 to |42 and would move outwards in the cylinder |42 thereby operating |39 in the reverse direction so that fluid under pressure is supplied through to |46 which would cause opposite rotation The fulloperation of the servo arrangement shown in Fig. 8 will be better appreciated from an explanation of the working of a full control system which -at the point of control consists of the instrument of Fig. 1 the shaft 2 of which is rigidly coupled to the shaft |41 of the arrangement of Fig. 8 and the terminals 3| and 35 of the Fig. 1 instrument are connected respectively to the 3| and 35 terminals of the'instrument of that the instrument of Fig. 1 at the point o! com trol has been calibrated to zero angular displacement of`its shaft 2 then vin Fig. 'I the ||9 impulses are coincident ,with the |20 impulses, the differential response |2| is zero, the Fig. 6 instrument provides no differential response, the valve arms |29 in Fig. 8 are in their mean positions and the valves |21-|28 and |29 are closed and the shaft |41 is not rotating. Now suppose that the shaft 2 at the signal producing instrument is accelerated` until it attains a constant angular velocity then, in effect, |20 in Fig. 7 would have a velocity to the right but |.|9 has no such velocity and therefore lags behind |20 so that there is a minus e/p error and the Fig. 6

Yinstrument will provide a diierentlal response such as I2 l, a current is therefore supplied to |02 in Fig. 8 which causes opening of the valve |21- |28 and the supply of fluid to |43 which causes openingA of the |38 valve and supply of fluid at pressure through |44 to |46 and |41 begins to rotate at which the I9 impulses in Fig. '1 will have a velocity in the samel direction as the |20 impulses. So long as there is a minus e/p error current will be supplied to |02 in Fig. 8 and therefore uid will be supplied in |43 causing continuously increased opening of the valve |33 and therefore acceleration of |41 and of ||9 in Fig. '1. So long as the velocityof ||9 is less than that of |20 in Fig. '1 the minus e/p error will grow,r the mean energy of the differential response will increase, the opening of the |21- |26 valve will increase, the rate of opening of |39 will increase and the rate of acceleration of |41 will increase, i. e. ||9 will be accelerated. As ||9 is being accelerated it will eventually have a velocity greater than that of |20 and the differential response of the instrument of Fig. 6 will gradually decrease, current to |02 in Fig. 8 will decrease, the opening of valve |21- |28 will decrease, the rate of opening of |39 will decrease and the acceleration of |41 will decrease until ||9 impulses are coincident with those-of |20 but as the velocity of ||8 is greater the latter will move into advance of |20, i. e. |I9 becomes |22, at which there will be a positive e/p error with a reversed response, such as |23, from the Fig. 6 instrument, a current will be supplied to |05 in Fig. 8, a reversed opening of |21-I 28, a reversed movement of |40, reduction of the opening of |39 Aand deceleration of |41 which will continue until the positive e/p error is zero. There may be repeated changes'as above described with the error first negative and then positive with repeated acceleration and deceleration of |41 but this will rapidly decrease in a few cycles of hunt of |41 until there is no e/p error, no response of the Fig.

6 instrument, no current to |02 or |05 in Fig. 8,

the valve |21-|28 will be closed, no iiuid now to or from |42 or |43, the valve |39 will have a constant opening and the shaft |41 will have a constant angular velocity and will be in synchronism and phase with the shaft 2 of the signal producing instrument. Any change of phase or angular velocity between |41 and the signal producing instrument shaft 2 will immediately bring corrective action such as described above and should the signal producing instrument shaft 2 change to another constant angular velocity in the same or the opposite direction |41 will do the same andn at any constant angular velocity of shaft 2 at the signal producing instrument the shaft |41 after cessation of corrective actions will have the same instantaneous f 17 |21-|28 will only operate when there is a difference of phase between |41 and the shaft 2 of the signal producing instrument, a diiference of i phase clearly being caused by some change of angular velocity if only momentary. Clearly the instrument of Fig. 1 together with the devices of Figs. 6 and 8` is means for instantaneouslyrelating a spatial magnitude, i. e. the angular displacement of |41, to the yt/p ratio of a signal.

The angular displacement of the shaft |48 of the valve |39 in Fig. 8 is a magnitude which is clearly related to the angular velocity o1' the shaft |41 but angular velocity `is the rate of change of angular displacement or the first diierential coeilicient with respect to time of angular displacement. The angular displacement of |48 may be linearly related to the angular velocity of |41 by suitable shaping of the valve opening, e. g. by the shaping of the annular groove segments in |28, provided the torque of the engine |48 is appreciably4 greater than the resistance of ,any load on |48 is a magnitude and like any other magnitude it can be related to a t/p ratio by the instrument of Fig. 1 by coupling I 48 to the shaft 2 of that instriunent.

The valve |39 as it is capable of differentiation in one case should be capable of extracting any one differential coefficient with respect to time, e. g. angular acceleration, rate of change of angular acceleration and so on. This may be accomplished by using a plurality of |39 valves in an arrangement such as that of Fig. 8 the first |39 valve directly controlling |46 and being itself controlled by the second |39 valve in the same manner as the |21|28 valve controls |39 in Fig. 8 by supplying fluid to the cylinders |42 and |41. Angular displacement ofv within its scope a large number of complex systems each of which performs one or a plurality of processes in automatic computation, such as a plurality of signal producing instruments as in Fig. 1 the signals of which are resolved into components, combined, modified. separated, recombined and/or changed in innumerable ways before use by one or a plurality df instruments as in Fig.1 for simple indication or with the addition of Fig. 6 or Figs.

6 and 8 for control each of which reproduces ay magnitude which may or may not be similar to any of the magnitudes related to the original signals; and one signal producing instrument the signal of `which is modified, resolved into compoynents which are modified, combined, separated,

resolved into components, recombined and/or changed in a variety of ways before use by one or a plurality of the indicating or controlling arrangements hereinbefore ldescribed each of which reproduces a different magnitude none of which may be the same as the original magnitude related to the first signal. No useful purpose can be served by describingdn detail all or any one of such -complex systemsy for each would comprise pluralities of the instruments and devices herein described and illustrated by the drawing by way of example and each would be |43, that second |39 valve would in turn be controlled by a third such valve and so on the last of the |39 valves being controlled by the |2`||28 valve. With one |39 valve there is instantaneous equality of angular displacements of the shaft |41 and the 2 shaft of the distant transmitter when angular velocity is constant, with two |39 valves there would be that equality with constant angular acceleration, with three |39 valves there would be that equality with a constant rate of change of angular acceleration, with four |39 valves there would be that equality with constant acceleration of the angular acceleration and so on. The angular displacement of the shaft |48 of any |39 valve is a magnitude which can be related to a t/p ratio according to the invention and each would be a diierential coefficient with respect to time and as such can be used in the invention for a number of useful purposes particularly in automatic computation.

The explanation of the invention hereinbefore has been limited to the most simple cases of signal production and signal use in indication and control by means of two sets of terminal apparatus between which is passed a single signal without consideration of any modification at any point between the two sets of terminal apparatus. Furthermore the instruments described have been of the most simple universal kinds limited to a minimum of geared stages in Fig. 1 and the minimum number of valves of simple character in Fig. 8. This has been done in order that the nature of the signal and precision and the general means for producing, conveying .between instruments and using such signals and precision shall be more readily comprehended but the invention is not limited to such simple cases and apparatus as it embraces bination of numbers numerical evaluation, and these will now be designed for a particular purpose or service to perform .a required kind of automatic computation, indication and control. Such complex systems however depend on modification and/or combination of signals, exactly as ordinary computation consists of modification and/or comor symbols capable oi described.

There are four principalchanges that can be made in signals which amount to multiplication, division, addition and subtraction of the t/p ratio of signals and therefore of the magnitudes represented by the ratios.. Fig. 9 shows graphically how division and multiplication can be achieved, |49 and |50 being the two component trains of impulses of, a signal. Taking |50 as the-reference component then in one common cycle of both components the impulse of |49 lags behind v the impulse of |50, i. e. there is a minus t interval of time, and the time interval is measured on the time-scale given by the period p of the common cycle of the two components in which the time interval is measured. As previously explained a magnitude is represented by the ratio minus t/p and the period of successive common cycles of the two components may vary continuously and erratically without altering the ratio t/p so long asthe magnitude is the same so that only change of magnitude will cause change of t/p,'e. g. in Fig. 1 the oscillator 40 may be unstable without affecting t/p. The reason for this is to be found in the phase-dis placers |0|| and |2|3 in Fig. 1 for the windings of are distributed through 360 degrees which is a spatial dimension which is quite independent of time and one cycle of variation of magnetic iield strength produced by the Windings is always exactly equal to 360 degrees whether the frequency of supply to is very low or infinitely high for frequency only decides sngularvelocity of one rotating magneticfneld which traverses d, l and Hequally. f

, In Fig. 9 if every second impulse of |49 and of 1501s suppressed then |48 becomes |5|I and |50 becomes |52. Within the limits of -precision of the signal the periods of two successive cycles of |40 and of |50 are equal and therefore the period of a common cycle of and |452 is twice .that of. one cycle of |50 but in that common cycle theA time interval' of displacement of the im'-- pulse of |5| from that of |52 is exactly the 'same as the time interval between an impulse of |49 from an impulse of |50 in a common cycle which 1S tbut the period 0f ISI- |52 is 2p if p is'theof the magnitude represented by |49-I50, i. e.

there has been division. Division by any integer may be accomplished in the same way by separating the two components of a signal and without Adisturbing the phase relation of the components selecting an equal sub-multiple freharmonic may be selected and used to add impulses to the com ponent and if this is done. with the two separated components of a signal then there will be multiplication of the' t/p ratio and therefore of the magnitude representedthereby. I

This is shown inFig. 9 in which the component |49 becomes the component |53 which is the third harmonic of |49 and |50 becomes |54 which is f also the third harmonic of |50 the time interval between the impulse of |53 and the impulse of |54 in a common cycle of |53| 54 being exactly equal to the corresponding interval t inthe |4S|50 signal but in the |53|54 Vsignal the period of the common cycle is p/3 if p is the period of the common cycle in the |49|50 signal and therefore the ratio of 14S-|50 is t/p compared to the ratio 3t/p of |53--|54, i. e. a. multiplication by 3 not only of the ratio but also of the magnitude represented by |53|54 relative to the magnitude represented by |49-|50.

By a combination of division and multiplication as above described it is possible to obtain a signal which represents a magnitude which is equal to the magnitude represented by the initial signal multiplied by any fraction, i. e. any ratio of the two magnitudes can be readily obtained.

The maximum value of a magnitude which can be represented in a signal according to the invention is strictly limited for t cannot be allowed to become greater than p, if it does then the ratio representing the magnitude will be :modemV ing t/p ratio of the signal tio ofthe angular movement of 2 relative to that cannot exceed the raof 2a. Again signals with which multiplication, division,vaddition and subtraction are to be performed may first be divided by a common factor in the manner described above and the final result multiplied by that factor.

A signal representing the sum or difference of two magnitudes can be readily obtained from combination of the two signals representing those magnitudes provided the signals. have a common component by separating the components of each signal and, neglecting the common component, the two uncommon components are combined to form a new signal which will represent the sum or difference of the magnitudes. This will be Yunderstood from Fig. lilin which |-|55 is a signal representing one magnitude and |55-|51 is the signal representing the other magnitude. the component |55 being common to both, i. e. |55 is produced by one oscillator so that frequency, phase and variations thereof are identical in both signals. Let it be assumed that the positive time interval is related to the magnitude in the |55-|51 signal and the time interval |6I, also positive, is related to the magnitude in the ease of the |55-|56 signal then period p being common to bothsignals because |55 is common the ratio |60/p of the |55-|51 signal and the ratio IBI/p of the |55- |56 signal become a ratio of (|60wl6il/p in a signal |5|--|'56, i. e. the ratio IGZ/p of the |58 signal represents a magnitude which is the diierence of the magnitudes represented by the |55- |56 and |55-|51 signals. The component |56 may be readily separated from the signal |55-|55 and the component |51 (xp-/p'in which x is any positive or negative the magnitudes are first related to t/p ratios of signals, for example in Fig. 1 an angular magnitude which at no time will exceed 360 degrees instead of being applied to the shaft 2 may be applied to the shaft 2a in which case the resultfrom the signal `|55|5'| by rectiiiersv |51 being reversed and combined with |56 to form the signal |58. w

The time interval |62 of the signal |58 is positive and'equal to the difference of the `two positive time intervals |60 and |6| and the combination of |56 with |51 to form a new signal will always result in a time interval which is the difference of the timeV intervals of the |55- |55 and |55-|51 signals, e.'g. if |50 and |6| are both negative then '|62 will be negative and the difference of |60 and IGI. This being so it follows that if one signal |55- 451 has a negative time interval such as |63 and the other signal |55-|55 has a positive time interval such as |6| then the result of combining |56 and |51 to form a new signal |59 means that the latter will have a time interval |64 which is the sum of |61 and |63 and therefore the ratio Nid/p is equal to |6| |63) /p and represents a magnitude which is the sum of the magnitudes represented by the signals |55-|56 and |55-|51. The t/p ratio of a signal may be made positive or negative at will for addition or subtraction as described above by the reversing switch I6 in Figs. 1 and 2.

Addition and substraction by combination of signals may also be performed in cases when there is not a common component of those sig nals provided the signals have a common timescale and a constant t/p ratio of one component of one signal and one component of the other signal, i. e. there is a constant phase' displacement between those components and both are produced by the same oscillator. Such would be the case in Fig. l0 if the |55 component of the |55-|56 signal had a constant time interval of displacement from the |55 component of the |55-|51 signal other things being the same. If that constant time interval is subtracted from the I 56 component then it may becombined with the |51 component to form a signal with a t/p ratio representing the sum or Vdiilference of the magnitudes represented by the |55`|56 and |55| 51 signals. This can be accomplished-by the instrument I of Fig. 1 used as previously described -as a receiver in remote indication, i. e.

the terminals |1 connected to terminals -20 and- ,termi'nals 23 connected to terminals' 26.

the. |55 component of the I55|51 signal would be applied to the terminals 34 and the |55 component of the |55|56 signal would be applied to terminals 3| and with switch 38 in correct position an indication would be provided by 'they tubes 36 and 31 of the time displacement of those components. By adjusting 21 and 28 the indication can be reduced to zero in 36 and 31 at which the |55' components are disconnected and the |56 component of thel I 55-PI56 signal is applied to the terminals 34 and the component appearing at terminals3l, which is the |56 component with the' constant time displacement subtracted, coinbined with the |51 component to form the new signal having a t/p ratio representing the sum or difference of the original magnitudes.

` Precision in addition and subtraction by combination of signals essentially requires that all of the signals are directly' or indirectly co'ntrolled by one master oscillation or train of impulses in order that the time-scales of all signals .be identical. It is possible to combine signals as described for addition and subtraction which are not controlled by a master oscillation pro- Flrst signal producer.

- 22 with Fig. 10 whichrepresen'ts the sum or difierence of the two magnitudes at will by using the switch I6 of one of the instruments. y

When the signal producers of two magnitudes ywhich are to be added. or subtracted are some to the position of the switch I6 of the second signal producer, the combination of the trains of impulses being in the manner shown in Fig. 10

with one position of the switch 39 of the second With the other position of that switch 39 the combination of the trains of impulses will be as shown in Fig. 11. vIn Fig. 10 if the magnitudes represented by I55-| 56 and |55|51 are both varying then the phase of both components of the combined signal |58 or |59 will be unstable and therefore such a combined signal cannot be combined with anf other signal for addition or subtraction as shown vided frequency and phase of the separate signals are closely controlledbut the possible preeision is very limited. When the frequency and phase and variations thereof of one componentV of each of two signals are not locked together then at least one of the signals must be converted. Such conversion means that the magnitude represented by the t/p ratio of the signal shall be reproduced and then again related to the t/p ratio of a new signal which is produced by using one component of the second signal. Reproduction of the magnitude requires a control arrangement such as Fig. 1 the shaft 2 of which is coupled to the shaft 41 of the arrangement of Fig. 8 with the Fig. 6 arrangement providing a diierential response for controlling the Fig. 8 arrangement. The shaft |41 of this'remote control arrangement would alsobe coupled to the shaft 2 of a second Fig. 1 instrument used as a signal producer, to the terminals 34 of which would be applied one component of the signal the t/p ratio of which represents a magnitude which it is desired to add to or subtract from the reproduced magnitude and the resulting sum or difference vwill be related to the t/p ratio of of a new signal formed by combining the remaining component of the former signal with the component appearing at the terminals 3| of that signal producer.

In some cases magnitudes which are to beJ added or subtracted have adjacent signal producers such as Fig. 1 in which case the terminals 30 of both instruments or the terminals 29 of both instruments may be connected together so that their oscillators are locked in frequency and phase by a train of impulses in the former case and by the fundamentaloscillation in thelatter case. Thereafter the combination of the train oi impulses at the terminals 3| of one instrument with the train of impulses at the 3| terminals of the other instrument will produce a signal in the manner described in connection in Fig. 10 but the combined signal resulting from addition or subtraction as shown in Fig. 11 can be directly combined with another signal in the manner of Fig. 10, i. e. two pairs of magnitudes lmay be representedby two combined signals as in Fig. 11 and then those two signals may be directly combined. in the manner of Fig. 10 so that four magnitudes can be readily added and/ or subtracted.

In Fig. 11 the signal |65 has its negative component stable 'its positive component varying in phase with variation of the magnitude represented by the signal, i. e. with the time interval |68. That positive component is appliedto the terminals 34 Lof a signal producer such as Fig. 1

. which produces the signal |66 representing another magnitude so that the negative component of |66 is always in the same instantaneous phase as the positive' component-*of |65 whatever the time interval |69 between the two components of 66 may be and whatever the time interval |68 between the two components of |65 may be. By combining the negative component of |65 with the positive component of |66 a signal |61 is formed having a time interval |16 between its components which is the sum of the time intervals |68 and |69 and therefore |61 represents a magnitude which is equal to the sum of the two magnitudes represented by I 65 and I 66. If the positive component of |65 'is used to form a signal |1I which has a negative time interval |13 Fig. l2 shows an example ofwthe kind of apparatus for changing the frequency of a train of imlpulses by producing a new train of impulses at a harmonic or sub-harmonic frequency of the rst train of impulses such as is required in multiplication and division as hereinbefore described with reference to Fig. 9. The devices' of Fig. 12 'are chiefly the same as devices shown in Fig. 2 and arci similarly connected in a circuit as shown -in- Fig. ,5, i. e., devices as .used in the instrument I of Fig. 1 and comprise a multi-oscillator 40 ofvknown kind which supplies oscillations to phase-splitters 4l and 43 at different frequencies but in harmonic relation. The instrument 4| supplies polyphaseJ oscillations to a phase adjusting device 21 the output terminals 20 of which are connected to the defiecting plates of a cathode-ray tube 41 of the kind shown-in Fig. 3 a circular sweep being produced therein at'the frequency of the polyphase oscillations applied to its deiiecting plates. Similarly the instrument 43 supplies polyphase oscillations to a phase adjuster 28 to the terminals 26 ofA which are connected the deilecting plates of anment as a remote indicator the signal to be changed being applied to the terminals 33 thereof and-first one and then the other of the new components applied to the terminals 3| with the switch 39 first in one position and then in the other soV that the appropriate component of the signal controls the sweeps of the tubes 36 and 31, differences of time-phase between a new component and its corresponding component of the initial signal being corrected by adjustments of 21 and 28 of the Fig. 12 arrangements. The instrument of Fig. 12 constitutes a means for converting a signal by independently changing the fre-y y quencies of the components of that signal.

Some systems according to the invention may require the conveyance of two or more signals,

' say between a signal producing station and an inother cathode ray tube 48 which is also of the kind shown in Fig. 3 a circular sweep being produced therein at the frequency of the polyphase oscillations supplied by 43. The frequency of sweep of 41 is lower than that of 48 and the two cathoderay tubes are otherwise connected as shown in Fig. 5 the tubes 41 and 48 co-operating to produce a train of impulses across the resistor 86 and terminals 30 the frequency of the impulses being equal to that of the sweep of the tube 41 and 'the duration of each impulse is that of those in the target electrode circuit of 48. In Fig. 12 a signal is applied to the terminals |15 and only one component of the signal passes through the rectifier |16 the dicating or control station, the signals representing magnitudes which because of variation or other component therefore being conned'to the resistor |11 connected across the terminals |15. The component of the signal which passes through |16 is applied to the terminals 34 of 40 and therein controls the frequencies and phases of y oscillations supplied'to 4| and 43. The train of impulses applied to 34 is a'cosine series of harmonic frequencies the fundamental of which is at the frequency of those impulses and therefore if the frequencies of oscillations supplied to 4| and 43 are harmonics of that fundamental those oscillations are locked in time-phase and harmonic frequency relation to each other by the control of the train of impulses which is precisely what is required in multiplication as described with reference to Fig. 9. If the frequency of the oscillation supplied to 4| by 40 is to be a sub-multiple of the said fundamental, i. e. as is required in division as described with reference to Fig. 9, then that oscillation is produced from and controlled in frequency and phase by de-multiplication in of the train of impulses applied to 34 in the Well known manner so that in this case also the oscillations supplied to 4| and 43 are locked in time-phase and harmonic frequency relation to each other by the control of the train of impulses applied to 34.

The oscillator 40 in Fig. 12 may be provided with a selector control in the Well known form so that the frequency of the oscillation supplied to 4| can be adjusted at will to be any one of a number of sub-harmonic and/or harmonic frequencies of the fundamental oi the train of impulses applied to the terminals 34 so that division and/or multi- 65 more according to the precision required. In di- 70 vision and multiplication as previously described -two arrangements such as Fig. 12 would be required one for each component of the signal and the time-phase produced by each of the arrangements can be checked by use of the Fig. 1 instruother reasonscannot be combined as one magnitude represented by one signal. Each of .the plurality of signals would in such a case require an individual channel and several channels besides being inconvenient may result in. loss of relative precision between the signals and therefore of magnitudes reproduced therefrom, for example .the electrical constants of the channels may be different.' A special case in which a plurality of signals is necessary arises when extreme precision is required and frequencies and the limitations of transmission channels are such as render that precision impossible in one simple signal. In the instrument of Fig. l the number of tubes such as 45 and 46 which co-operate in producing one train of impulses which can be used is limited by the frequency of sweep of the last tube and the ability of a transmission channel to convey the resulting short duration impulses without broadening them for that would destroy precision. For example if the tube 45 has a sweep frequency of ten cycles per second and in each such tube the period of sweep is 100 times greater than the duration of the impulse produced in its target electrode circuit then the gearing between stages may be 100 to 1 so that if the period of sweep in the first tube is 0.1 second the period of sweepin a second tube will impulses of 10 micro-seconds duration and the precision required would necessitate the use of four such tubes then two Fig. 1 instruments may be used the shaft 2a of the first geared to the shaft 2 of the second instrument the terminals 30 of the two instruments being connected so that the oscillations of lboth instruments are locked in phase and frequency then each instrument will provide a signal at its 32 terminals and both signals will contain information relating to the same magnitude. If each instrument has two geared stages and the tubes throughout have a 100 to 1 ratio of sweep to impulse then the time interval of the signal of the first instrument represents the magnitude to an accuracy of 10 micro-seconds if the period of sweep of its rst tube is 0.1 second but the signal of the second instrument contains additional information relating to that time interval to an accuracy of 0.001 micro-second, i. e., it measures from 0.001 to 10 micro-seconds, though its impulse duration is 10 micro-seconds and the second instrument uses the same frequencies as the first instrument. The time-scale of the ratio t/p of the signal of the instrument is 10,000

f appear alternately.

greater than the time-scale of the ratio t/p of the signal of the second instrument. Still greater precision can be obtained by gearing a third instrument to the second instrument and so on.

A plurality of signals without losing individuality may be combined to form one signal provided that one component of each signal is in locked time-phase with one component of each of the other signals. This is accomplished by non-interfering interspersal of impulses of the components of the several sig'nals which are not in locked time-phase. The method will be better understood from Fig. 13 in which |18 and |19 are two signals the negative components of which are identical as they would be if locked in phase and frequency. The positive components of |18 and |19 are shown with alternate impulses suppressed in order that the method of combination shall be clearly understood though before such` suppression there would be a positive impulse in each, cycle of the negative component in each signal. Suppose that the time interval which is related to the magnitude in each signal is positive that is measured to the right of the negative impulse of |18 and |18 in the drawing then as previously explained a positive impulse cannot move out of its immediate cycle of the negative component whatever the value of the magnitude represented by the signal. The positive impulses suppressed in |18 are in cycles oi the common negative component in which the remaining positive impulses of |19 occur and the suppressed positive impulses in |19 are in cycles of the common negative component in which the remaining positive impulses of |18 occur and therefore as .the positive impulses cannot move out of their immediate cycles of the common component the remaining positive impulses of |18 and |19 may be added to form the positive component of the signal |80. The signals 18 and |19 as shown may be directly added so thatin eiect odd cycles of the original signal from which |18 is obtained by suppression of alternate positive impulses are combined with even cycles of the original signal from which |19 was obtained by like suppression and in the combined signal the t/p ratios of the two original signals are retained for they In a direct addition of |18 t'o |19-the common negative component would be retained and there would be no indication showing which of the two t/p ratios is related to the magnitude which was represented by the original signal of |18 or of |19. For this reason the negative component of the combined signal |80 is the negative component of |18 with alternate impulses suppressed in cycles in which its positive impulses are suppressed and therefore it is clear in |80 that positive impulses occurring in the first half cycle of its negative component are those from the 18 signal and positive impulses in the second half cycle of that negative component are from the |19 signal.

It will be appreciated that the preparation of signals for combination by interspersal as above described consists of dividing the frequency of each component of one signal by 2 if two signais are to be combined, by 3 for three signals and so on and the uncommon component of each of the other signals has its frequency divided by 2, 3 or so on according to the number of signais to be combined but the time-phases of the divided signals and the other positive components are not the same, i. e. with two signals 7l"v it is necessary that positive impulses may combined the second is displaced 180 degrees relative to the first signal in the combination and with three signals the second is displaced 120 degrees and the third 240 degrees relative to the rst and so on the relative phase displacement oi successive signal components in the combinationbeing 360 degrees divided by the number of signals combined. In this way each component train of positive impulses in the combined signal has an individual phase-range in which it can vary according to variation of the magnitude it represents in that signal and none of those phase-ranges overlap adjacent phaseranges. Provided there is no overlap of phaseranges it is not necessary that the phase-ranges be equal and in cases where in original signals the positive component may be displaced positively or negatively from the negative component such displacement be limited so that there is no overlap of phase-ranges in the combined signal. This is shown in Fig. 13 where 8| and |82 are signals in each of which be displaced either way from the negative impulses but positive displacement in 8| plus negative displacement in |82 or vice versa must not exceed 360 degrees, in fact it is preferable that the sum of those displacements -be always less than 360 degrees. The signal |8| is shown with a negative displacement and |82 with a positive displacement so that in the combined signal |83 two positive impulses occur in the one period of the common negative component of |8| and |82 but there will be no interference provided displacements in |8| and |82 are properly limited.

Fig. 14 which is generally similar to Fig. 2 shows the kind of instruments required for combining signals by interspersal one of the three similar instruments |84, |85 and |88 being used for changing the frequency of the component which is common to al1 of the signals to be combined, say |84, and |85 and |86 being used for equal changing of the other components of two signals which are to be combined. If there are three or more signals to be combined then one extra instrument for each signal above two will be required in addition to the three shown in Fig. 14. The common component of the signals, obtained by rectification such as is described with reference to Figs. 5 and 12, in such a case would be applied to the terminals |81 of |84 and the other component of one of the signals would be applied to the terminals |88 of |85 and the other` component of the second signal would be applied to the terminals |89 of |85. The instrument |85, which is similar to one component producing part of Fig. 2 and is identical with |84 and with 86, consists of a multi-oscillator such as 40, two phase splitters such as 4| and -43 and two phase adjusters (|90 and |9|) such as 20 and 26 in Fig. 2, and has the fundamental frequency of the train of impulses applied to its terminals |88 controlling the frequency and phase of two ocsillations in harmonic relation produced by the multi-oscillator one of which has a desired sub-multiple frequency relative to the frequency of the train of impulses applied to |88, the phase of which is controlled by a phase control |90, the phase of the other oscillation being controlled by the phase control |9| and the sub-multiple frequency is selected by the control |82 of known kind. A polyphase oscillation lat the sub-multiple frequency is applied to the deector plates of a cathode-ray tube |93 of the kind shown in Fig. 3 and polyphase oscillations at 'the harmonic frequency phase controlled by |9| are supplied to the deilecting plates of a similar cathode-ray tube i |94. Circular sweeps are produced in the tubes precision of the signals used therewith. The

trains of impulses produced co-operatively by the tubes of each of the instruments |84, |85 and |86 are then combined to form one signal as described with reference to Fig. 13, i. e. the new common component is. say, that produced by |85 and is the negative component and the other new components produced by |84 and |86 respectively form together the interspersed positive component of the signal. Fig. 14 therefore lconsists of three simplified instruments l of Fig. 1 as further explained by Figs. 2 and 5 the simplifcation in each being that the instrument does not contain the tubes 381, 31, 41 and 48 nor the individual circuits thereof but has addeda frequency selector, such as |92 in Fig. 14, to the lmulti-oscillator 48.

The arrangement of Fig. 14 as described above generates new trains of impulses the duration oi' the impulses may therefore be shorter than the duration of impulses of the original components and because of the separate instruments |84, |85 and |85 with their individual phase adjustments signals with unequal phase ranges may be readily combined by interspersal so that the arrangement of Fig. 14 is of general utility. Combination by interspersal can, however, be accomplished by suppression of impulses as described with reference to Fig. 13 and this can be accomplished by more simplemeans particularly in cases where the signals have equal phaseranges. For this purpose all that is required is one instrument, say |85, of the Fig. 14 arrangement which uses a modified cathode-ray tube |94. The modification is solely a matter of the shape ofthe target electrode 52 in Fig. 3 in the plane of sweep that shape being a sector of a. circular disc the angle of which is 360 degrees divided by the number of signals to be combined, preferably that angle less the angular sizeof the focused spot of cathode rays in the tube. One such modified tube would be required for each signal to be combined and the instrument |85 in Fig. 14 would have the common component of the signals applied to its terminals |88, the appropriate sub-harmonic thereof would be selected by |92 and polyphase oscillations at the sub-harmonic frequency would be supplied to the deecting plates of each tube the phase oi sweep in each tube being adjusted by an individual phase-adjuster such as |9|. The tube |93, which may be unmodified as described above has the common component of the signals applied to its target electrode cathode circuit across one of two resistors in series therein. As the frequency of sweep in |63 is a sub-harmonic of the common component then by adjustment of |90 only one impulse per cycle of sweep will be permitted to flow from the target electrode to the cathode in |93 so that across the other oi 28 cuit would appear a train of impulses at the subharmonic frequency, i. e.l some of the impulses of the common component are suppressed. In exactly the same way the uncommon component of one oi.' the signals to be combined by interspersal would have some of its impulses suppressed in the tube |94 which has a sector target electrode which permits phase change of the unsuppressed impulses in accordance with change of the magnituderepresented by it and which impulse of the component in the cycle of sweep shall not be suppressed can be selected by ad` justment of |9|. Each of the signals to be combined would require an independent tube such as |94 for suppression of some of the impulses of its uncommon component and each such tube would have the sub-harmonic frequency of sweep and an individual phase-adjuster such as |9|.

The plurality of cathode-ray tubes |94 with sector target electrodes as described in the last paragraph above may 'be replaced by a single cathode-ray tubewhich has a plurality of independent target electrodes arranged in a ring coaxial with the sweep of the cathode-ray beam in the tube each of those electrodes being shaped as a sector'of the ring with a small gap between adjacent electrodes in the plane of the ring and therefore in the plane of the sweep. Such a tube would be connected as is |94 in Fig. 14 to |85 and supplied with polyphase oscillations at the sub-harmonic frequency which is supplied to |93 phase controlled by |9|. Each uncommon component of the signals to be combined would be applied to an individual target electrode circuit of the tube impulses of the component being suppressed as described in the last paragraph above.

Separation of the individual signals from a combined signal such as in Fig. 13 is readily accomplished by the apparatus of Fig. 14 the negative component of |80 being applied to the terminals |81 of |84 which supplies polyphase oscillations to one cathode-ray tube at a harmonic of the frequency of that component equal to the frequency of the original common component of the signals, i. e. the negative component of |18 and |19 in Fig. 13, and higher different harmonic frequencies of polyphase oscillations to each other cathode-ray tube connected to |84 all of the tube (go-operating as previously described to produce a new train of impulses at the frequency of that original common component. The negative component of |80 would also be applied to the terminals |89 of the instrument |85 and polyph e oscillations at the frequency of that compone produced and applied through the phase-adjus Ik rs to a plurality of cathode-ray tubes each having a sector target electrode or through one phase-adjuster to one tube having a plurality of target electrodes as described above. The positive component of |80 would be applied to the grid of each tube and in each target electrode circuit would appear one individual component of an original signal, e. g. the positive component of |18 as shown in Fig. 13, each of which combined with the vnew common component reproduces one of the original signals separated from the others. Fig. 14 is a means for interspersing a plurality of signals and is also a means for separating individual signals from an interspersal of a plurality thereof.

The signal used in the invention as previously described herein has consisted of a negative train of impulses combined with a train of positive the said two resistors in the target electrode cirimpulses in the case of a simple signal and in 29V the case of a compound signal a train of negative impulses combined with a plurality of interspersed trains of positive impulses the frequencies of trains of impulses in one signal being, equal or in harmonic relation to each other. The

essential requirement is that the component' by combining one or more than one trainiof im- Y pulses with one oscillation or with a plurality of cillations of diierent frequencies, for example'in Fig. 1 the train of impulses at the terminals 3| may be combined with the oscillation at the terminals 29. In all of these cases distinctness yof components of a signal can be achieved by keeping components separate instead of or in addition to the other methods of achieving distinctness.

It is not essential i'n the invention that sweep in any cathode-ray tube be circular, i. e. angular, for linear sweep may also be used with the advantage that only one single phase oscillation which is at every point thereof in the cylindrical surface of 203 yand therefore if at zero angular displacement of 202 the needle |91 is midway between the limits of its traverse the linear magnitude of movement of |96 will always be equal to the sine of any angular displacement of 202 and if with |91 in the said mid-position angular displacement of 202 is 90 degrees then the linear magnitude ofl displacement of 96 will always correspond to the cosine of the angular displacement of 202. If displacement of |96 is always measured downwards in the drawing from its upper limit of movement then in those two cases is required for producing the sweep and only one pair of deecting plates o1 coils per tube but the circular sweep gives-higher'precision. Magnetic phase-displacers such as in Fig. l are not essential in the invention for electrostatic displacers of well known kinds may equally be used nor is it essential that movement in phasedisplacers be angular for the primary and secondary of a displacer may be distributed linearly in known manner so that linear movement of primary relative to secondary produces phase change. Angular. movements are, however, more simple, precise and universal but this means that magnitudes which are not angular must be converted into angular magnitudes before they can be related to a t/p ratio of a signal and in reproduction they are 'rst reproduced as angular magnitudes and then converted into original i'orm if apparatus such as that of Fig. 1 is used. The means required for such conversions is relatively simple some examples being illustrated in Figs. 15, 16 and 1'7 and others will be readily obvious to skilled persons. Some magnitudes such as temperature, pressure, electric voltage and current and the like which are not spatial magnitudes must also be related to spatial magnitudes, for instance by means of knownwmeasuring devices for such magnitudes, before they can be related to a t/p ratio of a signal.

In Fig. a Vframe |95 has slidably mounted therein a bar |96 which has a needle |91 under pressure of a spring |98 engaging in a groove |99 of a drum 200 the shaft 20| thereof being parallel to |96 and having bearings in |95. The groove |99 is a helix of uniform pitch and therefore the device of Fig. 15 is a means for linearly relating a linear magnitude of movement of |95 to angular displacement ofso that by coupling 20| to the shaft 2 of the instrument of Fig. l a linear magnitude can be related to a t-p ratio of a signal or reproduced therefrom.

In Fig. 16 a shaft 202 having bearings in |95 carries a drum 203 which has a groove 294 in which engages one needle |91 of the bar |9h` which is parallel to 292 and slidably mounted in the frame |95. The groove 204 bounds an elliptical plane in the drum 203 the edge of the linear magnitude of displacement of corresponds to the versed sine and coversed sine respectively of the angle of displacement of 202.

The second needle |91 in Fig. 16 engages in a groove 205 of a drum 206 nxed to the shaft 201 which has bearings in the frame |95 and is parallel to |96 and 202. The groove 205 is a helix having one full turn in an axial distance equal to the total possible movement of |99 and the helix hasv a continuous logarithmic change of pitch 111.360 degrees thereof and therefore angular displacement of 201 always corresponds to the logarithm of the linear magnitude of displacement` of |96 and, as |96 and |91 couple 203 and 206, the angle of displacement of 201 always corresponds to the logarithm of the versed sine or coversed sine of the angle of displacement of 202. Ii the helix 205 has one full turn in the lower half of the total movement of |99` and l a similar helix but of reversed pitch and of opposite hand is joined to the rst helix, i. e. the point of join of the two helices is axially in the mid-position of |96r and the helices change logarithmically from the join one to one end of 206 and the other the angle of displacement of 201 will always correspond to the logarithmic sineor cosine of the angle of displacement of 202.

In Fig. 17 the bar |96 carrying two needles |91 is slidably mounted in the frame |95 in which are bearings for the shaft 208 which is parallel to |96 and which has iixed to it the drum 2| 0 which has a helical groove 209 of one turn and uniform pitch in which engages one needle |91, the other needle |91 engaging in a groove 2|| of fixed to the shaft 2|3 which is parallel to |96 and to 208 and has bearings in |95. The groove 2|| comprises a plurality of relices joined end to end each of which has one full turn in the same axial length and the pitch of the helices varies equally and logarithmically in the same direction of the axis so that the total angle of vdisplaceniki'nt of 2|3 corresponds to the logarithm of the llinear magnitude` of displacement of 96 from the zero position thereof. Clearly the total angle of displacement of 2|3 also corresponds to the logarithm of the angle of displacement of 2|0. Integral multiples of 360 degrees in the total angle of displacement of 2|3 measured positively or negatively representing the characteristic of the logarithm and the remaining angle less than 360 degrees of that total angle of displacement measured positively representing the mantissa of the logarithm. If the shaft 2| 3 is coupled to the shaft 2 of one transmitter as in Fig. l and that shaft has a reduction gearing to the shaft 2 of a second such transmitter then the one transmitter will produce a signal representing the mantissa of the logarithm and the second transmitter will produce a signal representing the characteristic of u the logarithm and the two signals may be comto the other end of 206, then' the shaft 2|l8 of the first converter.

Y 31" bined by interspersal as described with reference to Fig. 13.

It will be evident that grooves in drums as shown in Figs. 15, 16 and 17 may have any desired shapes for the purpose of relating alinear or angular magnitude to an angular magnitude according to any mathematical function andit will be equally`evident that a plurality of such converters may be coupled to eachother for the same purpose, for example if a first converter as in Fig. 17 has its shaft 2I3 coupled to the shaft 20%. of a second such converter then the angular displacement of the shaft 213 of the second converter will correspond to the logarithm of the logarithm of the angle of displacement of Linearly relating the t/p ratio of a signal to the logarithm of an original magnitude considerably extends the usefulness of multiplication and division as described with reference to Fig. 9 and addition and substraction as described with reference to Figs. 10 and 11 for multiplication provides a t/P ratio which is linearly related to the logarithm of a power of the original magnitude and division a t/p ratio linearly related to the logarithm of a root of the original magnitude whilst addition or subtraction of two t/p ratios which are linearly related to logarithms of original magnitudes produces t/p ratios. which are linearly related to the logarithm of the product or quotient respectively of the two original magnitudes. Devices such as shown'in Figs. 15, 16 and 17 are means for relating one magnitude to another magnitude according to a mathematical function which can be used in any part of the system of automatic computation by coupling the shafts of Figs. 15, 16 and 17 to any of the shafts 2 and 2a of Fig. 1 and Ill and |48 of Fig. 8.

The examples of methods and means employed in systems according to the invention as described herein show the exceedingly wide utility of the invention. The scope of the invention ranges from the most simple system for indication, control or automatic computation to the most complex system which combines indication, control and automatic computation of the most involved kinds and comprises many instruments which are adjacent and/or widely separated and with separated instruments linked by any tele- `graphic kind of communication channel. In

any system the general and/or instantaneous precision can be made as high as desired and any control can be powerful enough for moving with precision the largest bodies.

The mathematical processes in automatic .computation are not dependent on the continued .manipulations of one or more operators such manipulation being confined to initial adjustments of apparatus and thereafter the computation is wholly automatic and practically instantaneous or can be made so no matter how many constant and/or variable magnitudes enter into the computation and the mathematical processes which may be used in systems according to the invention are sufiicient for the automatic, practically instantaneous and most precise solution of most problems in mathematical analysis and synthesis. The fact that systems for automatic computation are not limited by space or time means that any number of individual systems according to the invention may be linked to cooperate in the solution of important problems which hitherto could not be attempted because ot the great amount of work involved.

I claim: y

1. A discovery of automatic computation employing remote indication and control in which a magnitude is represented by'an intermittent signal consisting of two distinct components so that each of a sequence of instantaneous values of the magnitude is related to an individual ratio oi.' time intervals in4 a sequence thereof contained inI said signal said two sequences and one said component `having identical frequencies and each said ratio is that of the time interval between a variation of one component and one of a pair of successive variations of the other component to the time interval between said pair of variations said variation being intermediate in time to said pair of variations, each said component being produced by an individual generator, both generators being controlled by a common oscillator to maintain the frequency relation of the two components said representation being achieved by means for time displacing one component relative to the other to an extent that each said ratio corresponds to an instantaneous value of the magnitude, evaluation of the magnitude represented by such a said signal in indication and control as the converse of said representation being achieved by means for automatically adjusting the instantaneous value of a spatial magnitude to correspond to a ratio of time intervals in the signal.

2. A discovery of automatic computation employing remote indication and control in which a magnitude is represented by an intermittent signal consisting of two distinct components so that each of a sequence of instantaneous values of the magnitude is related to an individual ratio of time intervals'in a sequence thereof contained in said signal said two sequences and one said component having identical frequencies and each said ratio is that of the time interval between a variation of one component and one of a pair of successive variations of the other component to the time interval between said pair of variations said variation being intermediate in time to said pair of variations, each said component being produced by an individual generator, both generators being controlled by a common oscillator to maintain the frequency relation of the two components the generator of one component comprising a plurality of impulse generators each of which is controlled in frequency and phase by an individual oscillation the plurality of said oscillations having their frequency relations maintained by said common oscillator said plurality of impulse generators beingr in a series arrangement in which one generator is controlled by the impulses of the preceding generator and the last generator in the series produces the said one component as a train of impulses the frequency of which is equal to the least common multiple of the frequencies of said plurality of oscillations and the duration of an impulse in said train is decided by the impulse generator operated at the highest frequency, said representation being achieved by means for time displacing one said component relative to the other which comprises means for relating the magnitude to a plurality of spatial magnitudes on individual scales each of which is the relative displacement between members of a phase displacing device individual to one of said plurality of oscillations a change of the magnitude thereby producing corresponding changes of phase of each of said plurality of oscillations and therefore a time displacement of said train of im- 

